The present invention relates to an apparatus for controlling an A.C. powered elevator.
In an A.C. elevator, an induction motor is used as an electric motor for driving an elevator cage, and the output of a variable frequency power source is supplied to the induction motor to vary a slip frequency, thereby controlling the torque of the motor. A process is proposed, according to the invention, for controlling the frequency and the current of a power source for so applying power to an induction motor that no regenerative power is generated in the induction motor at the time of braking the induction motor in the operating of an A.C. powered elevator.
FIGS. 4 and 5 are a circuit diagrams showing a conventional apparatus for controlling an A.C. powered elevator and a simple equivalent circuit diagram of an induction motor for explaining the process for preventing the regenerative power, disclosed in Japanese Patent Laid-open No. Sho 61-224888. In FIG. 5, symbols l.sub.1, l.sub.2 designate leakage inductances at primary and secondary sides, symbols R.sub.1, R.sub.2 denote primary and secondary side resistors, symbol S is a slip, and symbols V, I are a voltage applied to the induction motor and a current flowing through the induction motor.
Here, when the slip S is as represented by the following equation (1), EQU S=-R.sub.2 /R.sub.1 ( 1)
its mechanical input power Pm becomes as represented by the following equation (2), ##EQU1## where m is the number of phases. Since the power P.sub.E consumed in the induction motor is as represented by the following equation (3), EQU P.sub.E =m(R.sub.1 +R.sub.2) I.sup.2 ( 3)
the mechanical input power becomes equal to the consumed power in the induction motor. Therefore, when the induction motor is driven in the slipping state to satisfy the equation (1), no regenerative power is generated from the induction motor, and it is not necessary to supply power to the induction motor.
On the other hand, the torque T generated from the induction motor becomes as represented by the following equation (4). ##EQU2## where .omega..sub.r the rotating angular velocity of the rotor, .omega..sub.o is the input frequency, and p is the number of poles of the induction motor.
However, the rotating angular velocity of the rotor of the induction motor becomes as represented by the following equation (5). ##EQU3## When the equation (1) is substituted in the equation (4), the following equation (6) is obtained. ##EQU4## When the equation (1) is substituted in the equation (5), the following equation (7) is obtained. ##EQU5## More specifically, when the input frequency .omega..sub.o is controlled in the state for satisfying the equation (7), no regenerative power is generated from the induction motor, and the torque T at this time is given as represented by the equation (6).
FIG. 4 shows an example exemplified by the above-mentioned controlling process. In the drawing, reference numeral 1 designates a subtractor for subtracting the actual speed signal .omega..sub.r output from a tachometer generator 14 to be described later from the speed command signal .omega..sub.p, numeral 2 a control compensator for compensating the output signal of the subtractor, and numeral 3 a power drive side current command generator which inputs the torque command signal T output from the control compensator 2 and the actual speed signal .omega..sub.r and outputs a current command value I at the time of power driving operation. Numeral 4 designates a brake side current command generator which inputs the torque command signal T and the actual speed signal .omega..sub.r and outputs a current command value I.sub.B at the time of braking. Numeral 5 designates a switch for selecting the current command value I.sub.B at the time of power drive or the current command value I.sub.b at the time of braking to be switched in response to the polarity of the torque command signal T output from the control compensator 2. Numeral 6 designates a subtractor for subtracting the current value output from a current detector 15 to be described later from the current command value I.sub.A or I.sub.B selected by the switch 5, numeral 7 a pulse-width modulator which inputs the output signal of the subtractor 6 and pulse-width-modulates the output signal, and numeral 8 an inverter controlled by the output of the pulse-width modulator to drive the induction motor 9 as a variable voltage variable frequency power source. Numeral 10 designates a sheave rotatably driven by the induction motor 9, and numeral 13 a wire the ends of which are coupled to a cage 11 and a weight 12, and which is wound on the sheave 10. Numeral 14 designates a tachometer generator for detecting the rotating speed of the induction motor 9, and numeral 15 a current detector for detecting a current flowing to the induction motor 9.
In the apparatus for controlling the A.C. powered elevator constructed as described above, when the torque command signal T output from the control compensator 2 which inputs the output signal of the subtractor 1 for subtracting the actual speed signal .omega..sub.r from the speed command signal .omega..sub.p is positive, i.e., power drive torque is generated, the switch 5 selects the current command value I.sub.a generated from the power drive side current command generator 3 which inputs the torque command signal T and the actual speed signal .omega..sub.r. The output signal fed through the switch 5 is subtracted by the subtractor 6 by the output signal of the current detector 15, and the current command necessary to compare it with the actual current is then supplied to the pulse-width modulator 7. The pulse-width modulator 7 controls the inverter 8 in response to the necessary current command, thereby optimally controlling the current supplied from the inverter 8 to the induction motor 9 to thus control the generated torque.
Then, when the control torque that the torque command signal T generated from the control compensator 2 becomes negative, the speed command signal .omega..sub.o is obtained by the equation (7) from the speed signal .omega..sub.r. On the other hand, the following current I is obtained by the equation (6) from the torque command torque T. ##EQU6## Therefore, the brake side current command generator 4 generates the current command value I.sub.B obtained by the equations (7) and (8), which value is supplied through the switch 5 to the subtractor 6. The subtractor 6 supplies the difference between the current command value I.sub.B and the actually measured value supplied from the current detector 15 through the pulse-width modulaor 7 to the inverter 8, which, in turn, controls the current value to be supplied to the induction motor 9 as a target value.
However, when the torque command signal T is shifted from the power drive side to the brake side in the above-mentioned controller, if the input frequency .omega..sub.o of the induction motor 9 is varied to the value designated by the equation (7), the induction motor 9 generates a transient torque ripple, and the ripple frequency becomes equal to the slip frequency .omega..sub.s of the induction motor 9 designated by the following equation (9). EQU .omega..sub.S =.omega..sub.o -P.omega..sub.r ( 9)
When the equation (7) is substituted in the equation (9), the following equation (10) is obtained. ##EQU7## The reason why the equation (1) in which the torque ripple frequency becomes equal to the slip frequency .omega..sub.s is satisfied will be described. The basic equation of the squirrel-cage induction motor is represented as the following equation in the coordinates of orthogonal axis d--lateral axis q fixed to the stator. ##EQU8## where v.sub.ds : primary d-axis voltage
v.sub.qs : primary q-axis voltage PA1 i.sub.ds : primary d-axis voltage PA1 i.sub.qs : primary q-axis current PA1 i.sub.dr : secondary d-axis current PA1 i.sub.qr : secondary q-axis current PA1 K.sub.1 -K.sub.5 : constants PA1 .phi..sub.2d (0): d-axis secondary magnetic flux immediately before switching PA1 .phi..sub.2q (0): q-axis secondary magnetic flux immediately before switching PA1 .omega..sub.S : slip angle frequency (=.omega..sub.o -p.omega..sub.r)
R.sub.1 : primary resistance PA2 R.sub.2 : secondary resistance PA2 L.sub.1 : primary self-inductance PA2 L.sub.2 : secondary self-inductance PA2 M: primary secondary mutual inductance PA2 P: differentiation operator (=d/dt) PA2 P: pole logarithmic number PA2 .omega..sub.r : rotating angular velocity of the rotor
The generated torque T is represented by the following equation (12). EQU T=p(.phi..sub.2q i.sub.dr -.phi..sub.2d i.sub.qr) (12)
where .phi..sub.2d, .phi..sub.2q are d-axis and q-axis secondary magnetic fluxes to be represented as below. EQU .phi..sub.2d =Mids+L.sub.2 dr (13) EQU .phi..sub.2d =Miqs+L.sub.2 iqr (14)
When the equations (13) and (14) are substituted in the third and fourth lines of the equation (11) and i.sub.dr and i.sub.qr are erased, the following equations (15) and (16) are obtained as below. EQU (R.sub.2 +PL.sub.2).phi..sub.2 d-MR.sub.2 i.sub.ds +.omega..sub.2 L.sub.2 .phi..sub.22q =0 (15) EQU (R.sub.2 +PL.sub.2).phi..sub.2q -MR.sub.2 i.sub.qw .omega..sub.2 L.sub.2 .phi..sub.2d =0 (16)
When the equations (13) and (14) are similarly substituted in the equation (12), the following equation (17) is obtained. ##EQU9## Assuming that the primary currents i.sub.u, i.sub.v, i.sub.w immediately after the torque command signal T is altered from the power drive side to the brake side are represented as below for the simplification, ##EQU10## the d-axis and q-axis primary currents i.sub.d, i.sub.q become respectively as below ##EQU11## When the differential equations of the equations (15) and (16) are solved under the conditions that the rotating angular velocity of the motor immediately after switching is constant, .phi..sub.2d, .phi..sub.2q respectively become as represented by the following equations (20) and (21). ##EQU12## where .omega..sub.2 : P.omega..sub.r
When the equations (20) and (21) are substituted in the equation (11), the torque T becomes as below. ##EQU13## where K.sub.6 -K.sub.9 : constants
As apparent from the equation (23), it is understood that the torque ripple of the frequency equal to the slip angle frequency .omega..sub.S is transiently generated at the torque generated in the motor.
The slip angle frequency .omega..sub.S at the time of braking is given by the equation (10). When the rotating speed of the motor at the time of full speed is, for example, 1800 r.p.m. in an elevator of 60 m/min. of speed, if the power drive is switched to the brake at the time of full speed, the absolute value of .omega..sub.S becomes as below in the motor of p=2. ##EQU14## In other words, the motor generates a torque ripple of 30 Hz.
The transfer function of a machine system of an elevator, and particularly of a rope system is generally represented as shown in FIG. 6. More specifically, an ordinate axis indicates .omega.(=2.tau.f)/T dB, and an abscissa axis indicates the frequency. It is understood from FIG. 6 that a gain is high in a range that the frequency f is low and low in a range that the frequency f is high. However, since the gain is not so low at the vibration of approx. 30 Hz, the vibration is transmitted into the cage, resulting in a reduced riding comfort.